Depending when you are travelling its nearly always cheaper to buy on-line in advance.
You can pay instantly and chose ticket on departure which will allow you to put your credit card in a machine at the station and obtain your already purchased tickets. (If you are going from a major station)

You didn't say whether or not you're going back by train? Could be that you're getting a lift back, I don't know.

But advance tickets usually cheaper. Looking at Thursday now, from Cardiff to Manchester, there is a choice of £23 or £27 for advance tickets, depending on the time of travel, or a standard day single which is £48.30.

Also, do you plan on using the train often? A Rail card, at the cost of £20, can save huge amounts of money over a year.

Annnd, when planning a journey, don't just check the "direct" route, ie "Cardiff to Manchester". Try breaking the journey into separate legs. Sometimes that can work out cheaper too. For example, with Cardiff to Manchester change, some change at Bristol. You can get a single to Bristol for £3 and a ticket from Bristol to Manchester for £16, total = £19. You just need to be careful of matching up change over times.

Usually, buying a return ticket is beneficial, but looking at the Cardiff to Manchester on Thursday, the return is £58.60.

Ooh yes, and if you book over the internet, you can pick them up from the station (provided it is open (the size of Cardiff I imagine it would be) or there is a ticket machine). There is usually a 50p charge for this.

Return, Cardiff - Manchester. £30.40.
Bought today from the train kiosk.
I have a young person railcard.
Online it would have been 38.80 with 2x50p charges (One for using my card, one for fast ticket pickup using the machine)
Plus train ticket insurance incase services are cancelled which is £1 each way.

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Timing and flexibiliy is the key to save money.
You could have got two advance single tickets using your rail card
Cardiff to Manchester £8:00
and back for as little as £6.60

£14.60 in total - No insurance or collection charges - see the link I posted earlier.

That is assuming you could catch the very early morning train (04:00) and come back on the 20:34.

All easily found out on the internet. I have worked on many of the point of sale software products in stations and know for a fact that the cheapest fares are not always imediately apparent to the ticket office staff. (the screens usually default to the most popular, purchase now tickets for the chosen route)

Di is quite correct if you put in the time on the net, order in advance and are flexible as to when you travel you can get real bargains.
Of course you could find what you want on the internet and then ask for that at the station - but that will usually mean 2 trips to the station - 1 to buy your ticket in advance and 1 to board the train at a later date.

I can be quite smug about rail travel as I get free rail travel for myself and family as my firm used to be part of the railways pre-privatisation.

Timing and flexibility is the key to save money.
You could have got two advance single tickets using your rail card
Cardiff to Manchester £8:00
and back for as little as £6.60

£14.60 in total - No insurance or collection charges - see the link I posted earlier.

That is assuming you could catch the very early morning train (04:00) and come back on the 20:34.

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Good point there: when my son and I were flying up to Newcastle for a SASWE weekend, we checked on prices online in the evening, but did not have enough money in the relevant account to book at that time. By the time we were able to buy the tickets the next day, that cheapest price was no longer available, adding some £10 to the price.

It is normally cheapest to book as early as possible, bearing in mind that Advance tickets are normally only available three months ahead of the journey date, and numbers may be very limited. You will find, however, that the lowest prices depend on you guaranteeing to catch a particular train, and as is pointed out above, this may involve some unsociable hours to get the best deal.

They are currently in the process of simplifying the range of tickets available, removing lots of the named offers made by the individual companies, which some people found confusing.